As the Divine Hiddenness argument stands, it is not necessarily asking for evidence of God's existence that is public. This is wise because it may not be necessary, or even the best way for God to provide human beings with warranted knowledge of His existence, all things being equal. Here is a religous epistemology developed by William Lane Craig that speaks to why God would make belief in Him warranted primarily in a properly basic manner, and secondarily in an evidential manner:
http://www.rfmedia.org/av/video/christian-apologetics-who-needs-it-ccac07/
http://www.rfmedia.org/av/video/christian-apologetics-who-needs-it-ccac07/